**Simplifying algebraic expressions examples :**

To simplify algebraic expression, we need to follow the steps given below.

- Remove parentheses by multiplying factors.
- Use exponent rules to remove parentheses in terms with exponents.
- Combine like terms.
- Combine the constants.

**Example 1 :**

Simplify the expression

4a + 2b + a

**Solution :**

= 4a + 2b + a

By combining the like terms

= 4a + a + 2b

= 5a + 2b

**Example 2 :**

Simplify the expression

x^{2} + 3x + 2x + 5x^{2}

**Solution :**

= x^{2} + 3x + 2x + 5x^{2}

Combining the coefficients of "x^{2 }"and "x"

= x^{2} + 5x^{2 }+ 3x + 2x

= 6x^{2} + 5x

**Example 3 :**

Simplify the expression

4a^{3} + 6a + 3a^{3} + 8a

**Solution :**

= 4a^{3} + 6a + 3a^{3} + 8a

Combining the coefficients of "a^{3}^{ }"and "a"

= 4a^{3 }+ 3a^{3 } + 6a + 8a

= 7a^{3 }+ 14a

**Example 4 :**

Simplify the expression

6x + 2(2x + 7)

**Solution :**

= 6x + 2 (2x) + 2 (7)

= 6x + 4x + 14

= 10x + 14

**Example 5 :**

Simplify the expression

5n + 4(3n + 9)

**Solution :**

= 5n + 4(3n) + 4(9)

= 5n + 12n + 36

= 15n + 36

**Example 6 :**

Simplify the expression

3(x + 2y) + 4(3x + y)

**Solution :**

= 3(x + 2y) + 4(3x + y)

= 3(x) + 3(2y) + 4(3x) + 4(y)

= 3x + 6y + 12x + 4y

= 3x + 12x + 6y + 4y

= 15x + 10y

**Example 7 :**

Simplify the expression

3.2(x + y) + 2.3(x + y) + 4x

**Solution :**

= 3.2(x + y) + 2.3(x + y) + 4x

= 3.2(x) + 3.2(y) + 2.3(x) + 2.3 (y) + 4x

= 3.2 x + 3.2 y + 2.3 x + 2.3 y + 4x

= 3.2 x + 2.3 x + 4x + 3.2 y + 2.3 y

= 9.5 x + 5.5 y

**Example 8 :**

Simplify the expression

3(4m + n) + 2m

**Solution :**

= 3(4m + n) + 2m

= 3(4m) + 3(n) + 2m

= 12m + 3n + 2m

= 14m + 3n

**Example 9 :**

Simplify the expression

6(0.4f + 0.2g) + 0.5f

**Solution :**

= 6(0.4f + 0.2g) + 0.5f

= 6(0.4f) + 6(0.2g) + 0.5f

= 2.4f + 1.2g + 0.5f

= 2.4f + 0.5f + 1.2g

= 2.9f + 1.2g

**Example 10 :**

Simplify the expression

3/4 + [(2/3) (s + 2t)] + s

**Solution :**

= 3/4 + [(2/3) (s + 2t)] + s

= 3/4 + [(2/3) (s) + (2/3)(2t)] + s

= 3/4 + (2s/3) + (4t/3) + s

= 3/4 + (2s/3) + s x (3/3) + (4t/3)

= 3/4 + (2s/3) + (3s/3) + (4t/3)

= 3/4 + (2s + 3s)/3 + (4t/3)

= 3/4 + 5s /3 + (4t/3)

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